Pat chicken thighs dry and season with salt and pepper. Set aside.
Cook bacon lardons until crisp and fat has rendered in a large Dutch oven or other heavy-bottomed pot over medium heat (I use a 3.5 quart braiser). Transfer lardons to paper towel lined plate with slotted spoon.
Place a single layer of chicken thighs, skin-side down into hot bacon fat. Cook until skin has browned, then turn to brown other side (about 8 minutes total). Transfer to platter and repeat with remaining chicken thighs.
Add shallots, onion, and garlic to pot; cook and stir until onion is translucent, about 5 minutes. Add mushrooms and thyme; cook and stir 5 minutes more. Stir in white wine and broth; bring to boil. Add chicken skin-side up and any accumulated juices along with lardons to pot (chicken should be; reduce heat to medium-low. Cover and simmer 30 minutes. Transfer chicken to platter.
Increase to medium-high heat and bring sauce to boil; cook 8 to 10 minutes more until sauce thickens. Stir in butter and season to taste with salt and pepper. Reduce heat and return chicken to pot; simmer until heated through, spooning some of the sauce over the top. Serve from Dutch oven or arrange on deep platter. Garnish with fresh thyme sprigs and parsley if desired.
Note that this make 4 generous servings. If you're serving vegetables and mashed potatoes, pasta or other filling sides, it would easily serve 6.